3.18.56 \(\int \frac {1}{5} (2+2 x) \, dx\)

Optimal. Leaf size=24 \[ x+\frac {1}{5} \left (5-e^5+2 x-(5-x) x\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.38, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {9} \begin {gather*} \frac {1}{5} (x+1)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(2 + 2*x)/5,x]

[Out]

(1 + x)^2/5

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} (1+x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 13, normalized size = 0.54 \begin {gather*} \frac {2}{5} \left (x+\frac {x^2}{2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(2 + 2*x)/5,x]

[Out]

(2*(x + x^2/2))/5

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fricas [A]  time = 0.63, size = 9, normalized size = 0.38 \begin {gather*} \frac {1}{5} \, x^{2} + \frac {2}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2/5*x+2/5,x, algorithm="fricas")

[Out]

1/5*x^2 + 2/5*x

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giac [A]  time = 0.24, size = 9, normalized size = 0.38 \begin {gather*} \frac {1}{5} \, x^{2} + \frac {2}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2/5*x+2/5,x, algorithm="giac")

[Out]

1/5*x^2 + 2/5*x

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maple [A]  time = 0.01, size = 7, normalized size = 0.29

method	result	size
gosper	\(\frac {x \left (2+x \right )}{5}\)	\(7\)
default	\(\frac {1}{5} x^{2}+\frac {2}{5} x\)	\(10\)
norman	\(\frac {1}{5} x^{2}+\frac {2}{5} x\)	\(10\)
risch	\(\frac {1}{5} x^{2}+\frac {2}{5} x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2/5*x+2/5,x,method=_RETURNVERBOSE)

[Out]

1/5*x*(2+x)

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maxima [A]  time = 0.37, size = 9, normalized size = 0.38 \begin {gather*} \frac {1}{5} \, x^{2} + \frac {2}{5} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2/5*x+2/5,x, algorithm="maxima")

[Out]

1/5*x^2 + 2/5*x

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mupad [B]  time = 0.03, size = 6, normalized size = 0.25 \begin {gather*} \frac {x\,\left (x+2\right )}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x)/5 + 2/5,x)

[Out]

(x*(x + 2))/5

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sympy [A]  time = 0.04, size = 8, normalized size = 0.33 \begin {gather*} \frac {x^{2}}{5} + \frac {2 x}{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2/5*x+2/5,x)

[Out]

x**2/5 + 2*x/5

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